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 Volume 2004, Issue 1, 2004
Learning and Teaching Mathematics  Volume 2004, Issue 1, April 2004
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Volume 2004 (2004)
Volume 2004, Issue 1, April 2004

From the editors
Authors: Mellony Graven and Marcus BizonySource: Learning and Teaching Mathematics 2004 (2004)More LessAs editors of the new AMESA journal Learning and Teaching Mathematics we are extremely excited about this first edition and hope and believe that the journal will grow to become a resource that mathematics teachers and educators consider to be a 'must have'. We believe that this first edition has some very exciting, interesting and thought provoking pieces which cover a range of educational issues, mathematics content areas and educational phases.

To the editors
Author I. CassimSource: Learning and Teaching Mathematics 2004, pp 3 –5 (2004)More LessIn this letter I would like to share some of my thoughts and views of the current process of curriculum transition. Curriculum 2005 was launched with much fanfare and aplomb in 1997 by the former Minister of Education, Professor S. Bengu. The launch by the democratically elected government of the day heralded the end of the fragmented, discriminatory education policies of the previous government. This signaled the beginning of a better education for the masses of South African society.

A Day in the Life of a Head of Department, a Grade 12 teacher and an NGO worker
Author Aloysius Stephen ModauSource: Learning and Teaching Mathematics 2004, pp 6 –7 (2004)More LessI was born at Boys Town, Magaliesburg and attended my primary school at the Sella Moreneng Primary School. I went on to further my studies at Pax High School in Pietersburg where I matriculated in 1983. In 1985 I enrolled for a University diploma in Education (UDE) which I completed in 1987. I started teaching at Pax High School from 1988.
In my first year of teaching I was given a Gr 12 mathematics class to teach. I was inexperienced but I took the challenge positively and at the end of the year the students passed. From then on I told myself that nothing is impossible even for a teacher who is from a rural area.

Introducing and teaching firstdegree equations
Author Tickey De JagerSource: Learning and Teaching Mathematics 2004, pp 8 –11 (2004)More LessWe should introduce most topics in mathematics by starting with problems, and introducing them in such a way that the class will find them interesting and so want to solve them. Do not tell the class that you are going to deal with equations. First let them do examples in which the need to solve equations arises naturally.

All cubic polynomials are point symmetric
Author Michael De VilliersSource: Learning and Teaching Mathematics 2004, pp 12 –15 (2004)More LessFor instance, a graph is considered point symmetrical in relation to the origin 0 when each point P of a graph, as shown in Figure I, has a corresponding point Q (also on the graph) under a reflection through 0 so that PO = OQ. Or equivalently in the plane, each point P of the graph can be mapped onto a corresponding point Q (also on the graph) by means of a halfturn (a rotation through 180 degrees) around O. Using the transformation formula for a half turn, it therefore follows that a graph is point symmetric in relation to the origin if y = j(x) <=> y = f( x); in other words if it remains invariant under a halfturn around the origin.

I have a dream  a vision for mathematics education
Authors: Sally Hobden and Anthea MattheeSource: Learning and Teaching Mathematics 2004, pp 16 –17 (2004)More LessProspective Mathematics teachers in the PGCE (Post Graduate Certificate of Education) programme at the University of Natal begin their Mathematics Education studies with a careful inward look at what they personally believe about the subject mathematics, and how it is best taught and learnt.

Review of a mathematics education website
Author Mellony GravenSource: Learning and Teaching Mathematics 2004, pp 18 –19 (2004)More LessLast year I began exploring Michael de Villiers' Mathematics Education website. Once I started I was hooked. I therefore arranged for my Post Graduate Certificate of Education (PGCE) mathematics methodology students to spend an afternoon exploring the website. They too became hooked and by the end of the session I needed to chase them out of the computer room. They were astounded at the amount and the range of resources that were freely available for them to access and use from the internet: and all were accessed easily from Michael de Villiers' web page. For this reason I thought it useful to share with the readers of this journal some of the key features of this website.

How do I teach fractions?
Author Mni MajolaSource: Learning and Teaching Mathematics 2004, pp 20 –21 (2004)More LessDealing with fractions requires a lot of understanding and meaning. The way we teach fractions has a great impact on the understanding of the concept. Most teachers of Mathematics used to call fractions as some number over another number (e.g. ½ is 'one over two'). Let's take the case of a half. If the whole is divided into two equal parts and then one part is taken or shaded, the taken or shaded part is normally called 'one over two' (or one out of two). Learners grasp the concept of fraction in this way and deal well with a lot of fractions in which they link the diagrams with representations in the form of numbers.

It's not zippo
Author Susan GoyaSource: Learning and Teaching Mathematics 2004 (2004)More LessOne of the major tasks in algebra is recognizing or creating l in any of its various disguises. We can help students to think algebraically by using precise mathematical language with students, and expecting them to do the same. Just like this student, some students think slashing numbers means crossing them out. Students need to understand mathematically why the numbers went away.

Reasoning and proof in Grade 10 mathematics
Author Lorraine LaufSource: Learning and Teaching Mathematics 2004, pp 23 –25 (2004)More LessIn this short paper I will explain how I attempted to teach the midpoint theorem, and its converse, to an above average grade 10 class of boys at a wellresourced independent boys' school. The approach I took is based on my belief in a socialconstructivist theory of learning: very simply, this means that learners actively construct their own knowledge, and their ability to do so is enhanced when they work together and communicate their understandings.

Setting some Olympiad questions
Author Marcus BizonySource: Learning and Teaching Mathematics 2004, pp 28 –30 (2004)More LessThe South African Mathematics Olympiad is organised by the SA Academy for Science and Arts in cooperation with AMESA and SAMS (the South African Mathematical Society). AMESA is responsible for the first draft of the First Round Junior and Senior papers. The present AMESA policy is that regions set the papers on a rotation basis, and this year it was the turn of the Western Cape to produce the Senior First Round paper (the Eastern Cape did the Junior paper). In this article I share some of my experiences of the process.

Home buying while brown or black : teaching mathematics for racial justice
Author Eric GutsteinSource: Learning and Teaching Mathematics 2004, pp 31 –34 (2004)More Less"So one question leads to another question, and then you have to answer four more, and those four questions lead to eight more questions. So I think that [racial disparity in mortgage lending] is not racism, but that leads me to the conclusion that if it was not racism, then why do they pay more money to whites? Is that racism?"  Vanessa (all students' names have been changed), grade seven.

A day in the life of ... Tune's story
Author Sean TuneSource: Learning and Teaching Mathematics 2004, pp 35 –36 (2004)More LessI had a HDE qualification and struggled to teach mathematics at a secondary school. My teacher training was for primary school and not for secondary school. Confidence in teaching mathematics was very little. My mathematical knowledge had "gaps" and I tried to teach mathematics in the way my mathematics teachers used to teach it.

Help wanted! : the journal's question and answer column
Source: Learning and Teaching Mathematics 2004, pp 37 –38 (2004)More LessHelp wanted! : the journal's question and answer column

Connecting loci with real life
Author Gerrit StolsSource: Learning and Teaching Mathematics 2004, pp 39 –46 (2004)More LessThe direct algebraic approach that is used in our classrooms is one of the reasons learners believe that loci is difficult to understand. It is important that the learners first understand what the term locus means and then try to visualise and draw it. After drawing the picture, the learners can try to describe the graph directly in terms of χ and γ. By doing it this way, we make loci more understandable and more enjoyable. It is often possible to determine the equation of the locus directly. Otherwise we can use analytical geometry to describe the geometric condition algebraically in terms of χ and γ. This approach gives the learners a chance to experience the power of analytical geometry.

Kids say and do the darndest things
Source: Learning and Teaching Mathematics 2004 (2004)More LessAs teachers we come across fascinating examples of learner misconceptions, learner innovative methods to solve problems and simply wacky and wild ideas. We want this journal to include learner's work and thinking. Please send these in to is for publication with some brief thoughts or questions that you have about such events.

Fermat's Last Theorem, Simon Singh (Fourth Estate, 1997) : book review
Author Marcus BizonySource: Learning and Teaching Mathematics 2004, pp 48 –49 (2004)More LessThis book is a gripping read, and while the author does not talk down to his readers, he also does not expect deep thinking from them, but by the end of it everyone is more knowledgeable and more in tune with mathematics.

Towards a generalized maths assignment rubric
Author Marcus BizonySource: Learning and Teaching Mathematics 2004, pp 49 –50 (2004)More LessWhile the need for rubrics, and the advantages they can give, is becoming clearer to us all now, it is still a difficult task to develop a rubric that works as planned and that rewards the things we see as important. Moreover, one seems to have to rethink the issue so often, according to the assignment one has set. What we really need is a general rubric that would be applicable for almost any assignment, whether it be homework, a tutorial, or a project, and what is presented on the next page is a first draft of something that might work. What I am hoping for is that several educators will try it out and then give feedback on which aspects of it worked for them and which need to be altered, or even what new aspects need to be brought in.